The digital twin of a physical system is an adaptive computer analog which exists in the cloud and adapts to changes in the physical system dynamically. This book introduces the computing, mathematical, and engineering background to understand and develop the concept of the digital twin. It provides background in modeling/simulation, computing technology, sensor/actuators, and so forth, needed to develop the next generation of digital twins. Concepts on cloud computing, big data, IoT, wireless communications, high-performance computing, and blockchain are also discussed.
Features
Provides background material needed to understand digital twin technology
Presents computational facet of digital twin
Includes physics-based and surrogate model representations
Addresses the problem of uncertainty in measurements and modeling
Discusses practical case studies of implementation of digital twins, addressing additive manufacturing, server farms, predictive maintenance, and smart cities
This book is aimed at graduate students and researchers in Electrical, Mechanical, Computer, and Production Engineering.
Author(s): Ranjan Ganguli, Sondipon Adhikari, Souvik Chakraborty, Mrittika Ganguli
Publisher: CRC Press
Year: 2023
Language: English
Pages: 251
City: Boca Raton
Cover
Half Title
Title Page
Copyright Page
Contents
Preface
Authors' Biographies
Chapter 1: Introduction and Background
1.1. Introduction
1.2. Modeling and Simulation
1.3. Sensors and Actuators
1.4. Signal Processing
1.5. Estimation Algorithms
1.6. Industry 4.0
1.7. Applications
1.7.1. Maintenance
1.7.2. Manufacturing
1.7.3. Smart Cities
Chapter 2: Computing and Digital Twin
2.1. Digital Twin Use Cases and the Internet of Things (IoT)
2.2. Edge Computing
2.3. Telecom and 5G
2.4. Cloud
2.4.1. Microsoft Azure
2.4.2. Amazon AWS
2.5. Big Data
2.5.1. Analytics with Big Data
2.6. Google Tensorflow
2.7. Blockchain and Digital Twin
Chapter 3: Dynamic Systems
3.1. Single-Degree-of-Freedom Undamped Systems
3.1.1. Natural Frequency
3.1.2. Dynamic Response
3.1.2.1. Impulse Response Function
3.2. Single-Degree-of-Freedom Viscously Damped Systems
3.2.1. Natural Frequency
3.2.2. Dynamic Response
3.2.2.1. Impulse Response and Frequency Response Function
3.3. Multiple-Degree-of-Freedom Undamped Systems
3.3.1. Modal Analysis
3.3.2. Dynamic Response
3.3.2.1. Frequency-Domain Analysis
3.3.2.2. Time-Domain Analysis
3.4. Proportionally Damped Systems
3.4.1. Condition for Proportional Damping
3.4.2. Generalized Proportional Damping
3.4.3. Dynamic Response
3.4.3.1. Frequency-Domain Analysis
3.4.3.2. Time-Domain Analysis
3.5. Nonproportionally Damped Systems
3.5.1. Free Vibration and Complex Modes
3.5.1.1. The State-Space Method
3.5.1.2. Approximate Methods in the Configuration Space
3.5.2. Dynamic Response
3.5.2.1. Frequency-Domain Analysis
3.5.2.2. Time-Domain Analysis
3.6. Summary
Chapter 4: Stochastic Analysis
4.1. Probability Theory
4.1.1. Probability Space
4.1.2. Random Variable
4.1.3. Hilbert Space
4.2. Reliability
4.2.1. Sources of Uncertainties
4.2.2. Random Variables and Limit State Function
4.2.3. Earlier Methods
4.3. Simulation Methods in UQ and Reliability
4.3.1. Direct Monte Carlo Simulation
4.3.2. Importance Sampling
4.3.3. Stratified Sampling
4.3.4. Directional Sampling
4.3.5. Subset Simulation
4.4. Robustness
Chapter 5: Digital Twin of Dynamic Systems
5.1. Dynamic Model of the Digital Twin
5.1.1. Single-Degree-of-Freedom System: The Nominal Model
5.1.2. The Digital Twin Model
5.2. Digital Twin via Stiffness Evolution
5.2.1. Exact Natural Frequency Data Is Available
5.2.2. Natural Frequency Data Is Available with Errors
5.2.3. Natural Frequency Data Is Available with Error Estimates
5.2.4. Numerical Illustrations
5.3. Digital Twin via Mass Evolution
5.3.1. Exact Natural Frequency Data Is Available
5.3.2. Natural Frequency Data Is Available with Errors
5.3.3. Natural Frequency Data Is Available with Error Estimates
5.3.4. Numerical Illustrations
5.4. Digital Twin via Mass and Stiffness Evolution
5.4.1. Exact Natural Frequency Data Is Available
5.4.2. Exact Natural Frequency Data Is Available with Errors
5.4.3. Exact Natural Frequency Data Is Available with Error Estimates
5.4.4. Numerical Illustrations
5.5. Discussions
5.6. Summary
Chapter 6: Machine Learning and Surrogate Models
6.1. Analysis of Variance Decomposition
6.1.1. Proposed G-ANOVA
6.1.1.1. Statistical Moments
6.2. Polynomial Chaos Expansion
6.3. Support Vector Machines
6.4. Neural Networks
6.5. Gaussian Process
6.6. Hybrid Polynomial Correlated Function Expansion
Chapter 7: Surrogate-Based Digital Twin of Dynamic System
7.1. The Dynamic Model of the Digital Twin
7.2. Overview of Gaussian Process Emulators
7.3. Gaussian Process-Based Digital Twin
7.3.1. Digital Twin via Stiffness Evolution
7.3.1.1. Formulation
7.3.1.2. Numerical Illustration
7.3.2. Digital Twin via Mass Evolution
7.3.2.1. Formulation
7.3.2.2. Numerical Illustration
7.3.3. Digital Twin via Mass and Stiffness Evolution
7.3.3.1. Formulation
7.3.3.2. Numerical Illustration
7.4. Discussion
7.5. Summary
Chapter 8: Digital Twin at Multiple Time Scales
8.1. The Problem Statement
8.2. Digital Twin for Multi-Timescale Dynamical Systems
8.2.1. Data Collection and Processing
8.2.1.1. Stiffness Degradation
8.2.1.2. Mass Evolution
8.2.1.3. Mass and Stiffness Evolution
8.2.2. Mixture of Experts with Gaussian Process
8.2.3. Algorithm
8.3. Illustration of the Proposed Framework
8.3.1. Digital Twin via Stiffness Evolution
8.3.2. Digital Twin via Mass Evolution
8.3.3. Digital Twin via Mass and Stiffness Evolution
8.4. Summary
Chapter 9: Digital Twin of Nonlinear MDOF Systems
9.1. Physics-Based Nominal Model
9.1.1. Stochastic Nonlinear MDOF System: the Nominal Model
9.1.2. The Digital Twin
9.1.3. Problem Statement
9.2. Bayesian Filtering Algorithm
9.2.1. Unscented Kalman Filter
9.2.1.1. Algorithm
9.3. Supervised Machine Learning Algorithm
9.4. High Fidelity Predictive Model
9.5. Examples
9.5.1. 2-DOF System with Duffing Oscillator
9.5.2. 7-DOF System with Duffing van der Pol Oscillator
Bibliography
Index
